Question

Решите систему уравнений

Answer 1

$\left \{ {{3\sqrt{x+y}-2\sqrt{x-y}=4} \atop {2\sqrt{x+y}-\sqrt{x-y}=3}} \right. \; ;\; \; ODZ:\; \left \{ {{x \geq -y} \atop {x \geq y}} \right. \\\\t=\sqrt{x+y}\; ,\; \; p=\sqrt{x-y}\\\\ \left \{ {{3t-2p=4} \atop {2t-p=3\, |\cdot (-2)}} \right. \; \; \oplus \; \left \{ {{3t-2p=4} \atop {-t=-2}} \right. \; \left \{ {{6-2p=4} \atop {t=2}} \right. \; \left \{ {{p=1} \atop {t=2}} \right. \\\\ \left \{ {{\sqrt{x-y}=1} \atop {\sqrt{x+y}=2}} \right. \; \left \{ {{x-y=1} \atop {x+y=4}} \right.$

$\left \{ {{2x=5} \atop {-2y=-3}} \right. \; \left \{ {{x=2,5} \atop {y=1,5}} \right. \; \\\\(x \geq y,\; x \geq -y\; \; \Rightarrow \; \; 2,5 \geq 1,5\; \; i\; \; 2,5 \geq -1,5)\\\\Otvet:\; \; (2,5\; ;\; 1,5)$